Latent variable crossover for k-tablet structures and its application to lens design problems

This paper presents the Real-coded Genetic Algorithms for high-dimensional ill-scaled structures, what is called, the ktablet structure. The k-tablet structure is the landscape that the scale of the fitness function is different between a kdimensional subspace and the orthogonal (n−k)-dimensional subspace. The search speed of traditional GAs degrades when a high dimensional k-tablet structure is included in the landscape of the fitness function. In this structure, offspring generated by crossovers are likely to spread wider region than the region where the parental population covers and this causes the stagnation of the search. To resolve this problem, we propose a new crossover LUNDX-m using only m-dimensional latent variables. The effectiveness of the proposal method is tested with several benchmark functions including k-tablet structures and we show that our proposed method performs better than traditional crossovers especially when the dimensionality n is higher than 100. A...

• Type: Conference
• Year: 2005
• Where: GECCO
• Authors: Jun Sakuma, Shigenobu Kobayashi
• Keywords: GECCO 2005, Genetic Algorithm, K-tablet Structures, fitness Function